Inverted Flight requires you to fly the plane upside down. You're given up to 2 minutes 20 seconds to complete this challenge.
You can perform a barrel roll by holding the left stick and tilting it all the way to the right or left. Once you've complete the barrell roll four times you'll then be required to hold the plane upside down for several seconds. It's fairly simple, you just have to remember that the controls are invited whilst you are upside down.